Additional property of interferometer symmetry

Joseph L. Horner Polaroid Corporation, Research Division, Cambridge, Massachusetts 02139. Received 20 October 1977. 0003-6935/78/0215-0505$0.50/0. © 1978 Optical Society of America. In a recent paper1 dealing with the piecewise generation

of interferometric gratings, the authors discovered an inter­esting symmetry property they used to categorize interfer­ometers. This property is the difference in the number of reflections undergone by the two interfering beams in reaching the plane by interference. It was shown in that paper that interferometers having an even difference can produce ex­tended gratings by translating a single mirror, but interfer­ometers having an odd difference cannot.

It is the purpose of this Letter to point out another conse­quence of this even-odd symmetry. Consider the two inter-

Fig. 1. Odd number reflections.

Fig. 2. Even number reflections.

ferometers shown. Figure 1 has odd symmetry, and Fig. 2 has even symmetry. If we keep track of the two sides of each beam, shown by a solid line and a dashed line, we will observe that in the even symmetry case (Fig. 2) the left side of one beam interferes with the left side of the other beam, and similarly with the right side. In the case of odd symmetry (Fig. 1), the right side of one beam interferes with the left side of the other beam, and vice versa. The implication of this is that odd symmetry interferometers require spatial coherence across the full width of the beam, but even symmetry ones do not. In fact, in this simple model no spatial coherence is re­quired for even symmetry interferometers.

Stephen A. Benton of this laboratory has pointed out to me that holographers have been aware of this effect and take care to arrange the number of reflections in the reference beam so a ray in one part of the object beam interferes with its coun­terpart in the reference beam to reduce the spatial coherence requirements.2

References 1. L. F. Mollenauer and W. J. Tomlinson, Appl. Opt. 16, 555

(1977). 2. R. E. Brooks, L. 0. Heflinger, R. F. Wuerker, and R. A. Briones,

Appl. Phys. Lett. 7, 92 (1965).

15 February 1978 / Vol. 17, No. 4 / APPLIED OPTICS 505